Know your audience.
Keep in mind that scholarship decisions are made by a committee often comprised of academic advisors, deans, and professors. Guide your essay towards this audience in a way that makes the information accessible. Providing sufficient background on the story can be helpful in making the essay clear. At the same time, select essay topics that cater to the audience, as well.
Answer the prompt.
At the end of the day, no matter how inspiring your scholarship essay may be, it has to answer to original question or stick to the prompt. When writing an essay, it is all too easy to get wrapped up in the excitement of a story and lose focus. To avoid this pitfall, use your conclusion to bring your story full circle.
Focus on a strong introduction.
This is the first thing the scholarship committee will read. A strong introduction will allow the committee to remember not only your application, but the feelings they felt when reading you essay. Your introduction should push the reader to continue to read. In a sense, it should convince them to hear your story all the way through. Consider possibilities outside of the traditional introductions (questions, definitions, quotes) such as figurative language or dialogue.
Get in your feels.
Pathos, pathos, pathos. Selecting a topic that you feel passionately about will allow your essay to read like a narrative rather than an essay. Hint: it also makes writing the essay a much more enjoyable experience. This essay may be the only way to allow the committee to get to know you, so your essay should be you on a page. Tell a story that makes your reader feel something: joy, excitement, empathy, hope.
Proofread and revise.
This is arguably the most important step in essay-writing of any kind. Submitting an error-free essay will show the committee that you took the time and effort to make your essay the best it could be. It also allows them to focus on the theme of your essay without the distraction of misspelled words or punctuation errors.
Best of luck, and get writing!